The dimensions of the shaft depend on many factors. The rules below will give an approximate selection. In borderline cases, please consult us. The questionnaires in chapter 12 will help you. We would be pleased to give you advice.

8.1 Selection of Joint Size for Stationary Drives

The part of the propeller shaft which determines its useful life is normally the joint bearing. So the joint size should preferably be determined from the transferable torque of the bearing. The calculation below is based on the standard roller bearing calculation, where the oscillating movement is regarded as replaced by a rotational one.

The dimension for the transferability of the bearing is the joint load rating T = C · R, where C is the dynamic transfer capacity of the bearing and R the distance of the bearing centre from the joint centre. The joint load rating is given in the data sheet for the shaft. Terf can be determined using the same equation. It applies to uniform operation, i.e. when the torque Md occurs throughout life Lh at rotation speed n and deflection angle ß.

A working machine with a small mass moment of inertia, which assumes a torque of 1000 Nm at n = 1 450 rpm, should be driven by an electric motor via a shaft running under a deflection angle of 7°. The life should be 2000 h. What joint size is required?

Solution:

Electric motor and impact-free working machine gives an impact factor of 1.0. Then:

So Terf is found to be 1339 Nm. From the data sheet, we now select the shaft with the next highest value. If we are to use a shaft of design 008 for example, the type and joint size 008 195 are selected with a joint transfer capacity of 1460 Nm.

For the joint found, we now check that

1000 Nm · 1,0 < 1460 Nm · cos 7° = 1449,1 Nm.

The condition is fulfilled, and the shaft can be used. It will achieve a life of:

In many applications, in particular in vehicles, the moment, the rotation speed and/or the deflection angle are not constant. We must then try to form classes to which moment, rotation speed and deflection angle can be allocated and determine their time proportions.

For an initial estimated joint size, the individual life can then be assessed for each class:

Where:

Lhn

=

individual life of class n, where n = 1,2,3...n

Mn

=

the moment allocated to class n

Tvorh

=

joint power factor of estimated joint size

nn

=

rotation speed allocated to class n

ßn

=

deflection angle allocated to class n

See above for other symbols.

From the individual life, the total life can be determined as follows:

where: q = time proportion in % Lh1...Lhn individual life in h.

8.2 Selection of Joint Sizes for Vehicle Drives

In this section, the following symbols are used:

MFG

=

function torque capacity (from data sheet)

MX

=

general dimensioning moment for a propeller shaft

MA,MB,MC

=

dimensioning moment for propeller shafts A, B, C

Mmot.

=

general proportional engine torque on propeller shaft

Mmotmax

=

max. engine torque

MRad x

=

general proportional wheel adhesion torque at propeller shaft

s

=

joint bearing safety factor = 1,5 < s <2,0

k

=

shock factor (see table above)

µR

=

tyre coefficient of friction = 0,6 < µ < 1,0

=

general gear efficiency

G

=

efficiency of engine gear

V

=

efficiency of transfer box

A

=

efficiency of final drive

iW

=

theoretical value for converter ratio

iWF

=

converter brake conversion

iG max

=

max. engine gear ratio (1st gear)

iG min

=

min. engine gear ratio (1st gear)

iV max

=

transfer box ratio (1st gear)

iV min

=

transfer box ratio (nth gear)

iA

=

final drive ratio

V

=

engine torque distribution ratio Tmot V / Tmot H

Rdyn

=

dynamic rolling radius of tyre

GV

=

front axle load; total front axle load

GV1

=

front axle load, 1st axle

GV2

=

front axle load, 2nd axle

GH

=

rear axle load; total rear axle load

GH1

=

rear axle load, 1st axle

GH2

=

rear axle load, 2nd axle

The function torque capacity MFG of the propeller shafts is given in the data sheets in this catalogue. This moment can be transferred by the propeller shaft for short periods at limited load frequency with 0° joint deflection angle.

With a joint deflection angle of ßº, the function limit moment is reduced by the factor cos ßº.

The function torque capacity MFG must be sufficiently larger than the dimensioning moment Mx.

MFG1,5 · Mx

The dimensioning moments Mx for the propeller shafts between the engine and the final drive are calculated approximately from the moments of the torque Mmotx exerted by the engine and the adhesion moment Mradx exerted by the wheel, as follows:

Mx = ½ (Mmotx + Mradx)

For propeller shafts A between the engine and the gearbox, the influence of the high rotation speed part and the engine shock factor must be taken into account.

If a converter is fitted, some special features should be observed:

If the propeller shaft is installed between the engine with converter and the gearbox, the impact factor s = 1 must be used. If the propeller shaft is between the engine and gearbox with a converter in front, the effect of the wheel moment = 0.

If the brake conversion iWF < 1,4, its influence can be ignored, so iW = 1.

If the brake conversion iWF > 1,4, its influence must be allowed for by a factor of 0.76, so iW = 0,76 · iWF.

8.3 Selection System for Propeller Shafts in Vehicles for Normal Use

Road Vehicle 4 x 2

Selection torque for propeller shaft A between engine 1 and gearbox 2.

These selections will avoid major dimensioning errors. However, they disregard important influences on the useful life such as deflection angle, rotation speed, loading, effect of dirt, temperature etc. For example, halving the deflection angle doubles the life, as 9.1 shows.

If special propeller shafts are produced with steel rotating rod, calculate the critical rotation speed as

where D = rod diameter and l0 = free length, all in mm.

These equations apply for smooth tubes or rods. propeller shafts only achieve around 80-90% of this speed because of play in bearings and sliding pieces and additional dimensions. As the max. operating speed should lie 10-20% below this critical speed, the operating rotation speed selected is:

noperation 0,6... 0,7 nkrit

The maximum operating speed can be taken from the diagrams below.

Fig. 24:

Propeller shaft with steel tube

Propeller shaft with steel rotating road

If the maximum operating speed is not sufficient, a larger tube diameter or rod design with centre bearings should be used.

8.5 Balancing Propeller Shafts

Propeller shafts for drive shafts in the automotive industry are dynamically balanced. Balancing is the equalization of weight of eccentrically running masses (Fig. 25) in the propeller shaft to achieve quiet running and reduce load on the joints and bearings in the connected assemblies.

Practical experience has shown that as the rotation speeds increase, a smaller shift in the centre of gravity can be permitted. It is therefore sensible to take the product of rotation speed x shift in centre of gravity as a value for the permitted imbalance. DIN ISO 1940 "Requirements for balance qualitites of rigid rotors" is also based on this concept. A table there gives "quality classes" for different components, where it has been assumed that there is no point in balancing the different elements (wheels, rims, wheel sets, crankshaft components, shafts etc.) of a closed machine group, e.g. a vehicle, to widely differing quality classes.

As repeated clamping gives different values due to play, the values of the equation only correspond 65% to the value permitted under DIN ISO 1940. In test runs with repeated clamping therefore, 135% of the value given in DIN ISO 1940 is permitted, i.e. approximately double the equation value.

In order to achieve adequate smooth running of the propeller shaft, the mass acceleration moment of the centre part between the joints must not be too large. The mass acceleration moment depends on the mass moment of inertia of the centre part, the rotation speed n and the deflection angle of the joint. The permitted size of the mass acceleration moment increases with the moment transferability of the joint, i.e. as the joint power factor T increases, the permitted mass acceleration moment M also increases.

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